and invert the relevant quantum Matone relation (REF ) in order to express \(a\)  as a function of \(u\)  and find \({\cal F}(a;m_f;q; \hbar )\)  (up to the one-loop term, that can be computed by other means [1]}, [2]}, [3]}). Finally one has to impose the quantisation on \(a_D\)  as an `eigenvalue' equation for \(\omega \) , whose solutions are functions of \(n\) , \(\ell \) , \(m\) 's, \(M\) , \(Q\) , \(J\) 's. In [4]}, [5]}, [6]} we checked agreement among qSW, Leaver and WKB for a wide variety of BHs and (bound-states of) D-branes.
